On the Number of Orthogonal Signals Which Can Be Placed in a $WT$-Product

We first introduce some notations and definitions and then state the problem. Throughout the paper, Q = 27rW > 0 and T > 0 will be fixed. In our discussion, we will lean heavily on the work of Slepian and Pollak [1] and will mainly use their notation and terminology. By ?2 we denote the set of all complex-valued functions absolutely square integrable on the whole real line (time) in the sense of Lebesgue. From now on all functions in question will be in 2' (note that these are precisely the time functions with finite energy). On 22 we define the operators D and B by